3 Description

The Schur factorization of A is given by

A=ZTZH,

where Z, the matrix of Schur vectors, is unitary and T is the Schur form. A complex matrix is in Schur form if it is upper triangular.

Optionally, nag_zgees (f08pnc) also orders the eigenvalues on the diagonal of the Schur form so that selected eigenvalues are at the top left. The leading columns of Z form an orthonormal basis for the invariant subspace corresponding to the selected eigenvalues.

5 Arguments

1:
order – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

Constraint:
order=Nag_RowMajor or Nag_ColMajor.

2:
jobvs – Nag_JobTypeInput

On entry: if jobvs=Nag_DoNothing, Schur vectors are not computed.

If jobvs=Nag_Schur, Schur vectors are computed.

Constraint:
jobvs=Nag_DoNothing or Nag_Schur.

3:
sort – Nag_SortEigValsTypeInput

On entry: specifies whether or not to order the eigenvalues on the diagonal of the Schur form.

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NE_SCHUR_REORDER

The eigenvalues could not be reordered because some eigenvalues were too close to separate (the problem is very ill-conditioned).

NE_SCHUR_REORDER_SELECT

After reordering, roundoff changed values of some complex eigenvalues so that leading eigenvalues in the Schur form no longer satisfy select=Nag_TRUE. This could also be caused by underflow due to scaling.

7 Accuracy

8 Parallelism and Performance

nag_zgees (f08pnc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

nag_zgees (f08pnc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the Users' Note for your implementation for any additional implementation-specific information.